Question

Consider the following equation:

cos x = x³
Use your calculator to find an interval of length 0.01 that contains a root. (Enter your answer using interval notation.)

Answer 1

To find an interval of length 0.01 that contains a root for the equation cos x = x³, use a graphing calculator and the zero function.

Step-by-step explanation:

To find an interval of length 0.01 that contains a root for the equation cos x = x³, you can use a graphing calculator. Follow these steps:

1. Enter the equation cos x - x³ in your calculator.
2. Use the zero function on your calculator to find the x-values where the function equals 0.
3. From the list of x-values, choose an interval of length 0.01 that contains a root. For example, if the x-values are -1 and 1, you can choose the interval [-0.99, -0.98] or [0.98, 0.99].

Therefore, an interval of length 0.01 that contains a root for the equation cos x = x³ can be represented using interval notation as [-0.99, -0.98] or [0.98, 0.99].